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"This book is devoted to the Beltrami equations that play a significant role in geometry, analysis and physics and, in particular, in the study of quasiconformal mappings and their generalizations, Riemann surfaces, Kleinian groups, Teichmuller spaces, Clifford analysis, meromorphic functions, low dimensional topology, holomorphic motions, complex dynamics, potential theory, electrostatics, magnetostatics, hydrodynamics and magneto-hydrodynamics.The purpose of this book is to present the recent developments in the theory of Beltrami equations; especially those concerning degenerate and alternating Beltrami equations. The authors study a wide circle of problems like convergence, existence, uniqueness, representation, removal of singularities, local distortion estimates and boundary behavior of solutions to the Beltrami equations. The monograph contains a number of new types of criteria in the given problems, particularly new integral conditions for the existence of regular solutions to the Beltrami equations that turned out to be not only sufficient but also necessary.The most important feature of this book concerns the unified geometric approach based on the modulus method that is effectively applied to solving the mentioned problems. Moreover, it is characteristic for the book application of many new concepts as strong ring solutions, tangent dilatations, weakly flat and strongly accessible boundaries, functions of finite mean oscillations and new integral conditions that make possible to realize a more deep and refined analysis of problems related to the Beltrami equations"

"This text presents differential forms from a geometric. The author approaches the subject with the idea that complex concepts can be built up by analogy from simpler cases, which, being inherently geometric, often can be best understood visually. The second edition includes a completely new chapter on differential geometry, as well as other new sections, new exercises and new examples. Additional solutions to selected exercises have also been included. "

"Differential geometry is the study of the curvature and calculus of curves and surfaces. A New Approach to differential geometry using Clifford's geometric algebra simplifies the discussion to an accessible level of differential geometry by introducing Clifford algebra. This presentation is relevant because Clifford algebra is an effective tool for dealing with the rotations intrinsic to the study of curved space."

"ABSTRAKOpsi saham merupakan salah satu jenis sekuritas derivatif yang nilai kontraknya bergantung pada nilai saham yang tercantum pada kontrak opsi. Opsi saham Asia termasuk ke dalam jenis opsi eksotik yang nilainya dipengaruhi oleh rata-rata nilai saham sepanjang masa hidup opsi. Dalam skripsi ini rata-rata nilai aset yang digunakan adalah rata-rata geometrik. Nilai saham yang digunakan dalam skripsi ini akan mengikuti model CEV Constant Elasticity of Variance yang merupakan bentuk umum dari model Black-Scholes yang terkenal. Dalam menentukan nilai opsi secara analitik dengan model CEV sangatlah sulit maka dari itu nilai dari opsi Asia dimodelkan ke dalam persamaan diferensial parsial. Persamaan diferensial parsial untuk opsi Asia nantinya akan diselesaikan dengan metode perturbasi. Metode perturbasi yang digunakan adalah metode perturbasi regular. Pada akhirnya akan dihasilkan formula untuk menentukan harga opsi call Asia dengan model CEV dan rata-rata geometrik

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ABSTRACTStock options are one type of derivative securities whose contract value depends on the value of the shares listed on the option contract. Asian stock options fall into the type of exotic options whose value is affected by the average share value throughout the lifetime of the option. In this thesis the average asset value used is the geometric average. The stock value used in this thesis will follow the CEV Constant Elasticity of Variance model which is a general form of the famous Black Scholes model. In determining the analytic option value with the CEV model it is very difficult, because of that the value of the Asian option is modeled into a partial differential equation. Partial differential equations for Asian options will be solved by perturbation method. The perturbation method used is a regular perturbation method. In the end a formula will be generated to determine the price of Asian call option with CEV model and geometric mean."

"This book contains survey papers based on the lectures presented at the 3rd International Winter School “Modern problems of mathematics and mechanics” held in January 2010 at the Belarusian State University, Minsk. The results discussed are application oriented and present new insight into applied problems of growing importance such as applications to composite materials, anomalous diffusion, and fluid dynamics."

"M. Cinquini Cibrario: Equazioni non lineari e teoria delle caratteristiche.- J. Leray: La théorie de L. Garding des équations hyperboliques lineaires.- S.L. Sobolev: Lezioni sulle equazioni iperboliche non lineari.- A Weinstein: Equazioni alle derivate parziali singolari."

"This book shows how to apply theoretical mathematical models to unravel the mechanisms involved in processes found in mathematical physics and the biosciences. It is a unique collection of abstract methods that deploy nonlinear partial differential equations. "